Честность помогает людям доверять друг другу.

It breaks down like this:

• Честность — the subject, in the nominative case
• помогает — helps, 3rd person singular present
• людям — to people, in the dative plural
• доверять — to trust, infinitive
• друг другу — each other, here in the dative form

So the structure is basically:

[Subject] + helps + [someone, dative] + [infinitive] + [object of the infinitive]

A very literal reading is:

Honesty helps people trust each other.

Because помогать normally takes the person being helped in the dative.

You ask:

помогать кому? — to help whom?

So:

• помогать другу — to help a friend
• помогать детям — to help children
• помогать людям — to help people

That is why you get людям, not люди or людей.

Yes. Людям is the dative plural form of люди.

This is a useful thing to notice because люди is an irregular noun. It is the plural form used for people, historically related to человек.

Some forms are:

• люди — people
• людей — of people / people in accusative for animate nouns
• людям — to people
• людьми — by/with people

So людям is just the form required by помогать.

Because Russian often uses this pattern:

помогать кому-то делать что-то
to help someone do something

So:

• помогать детям учиться — to help children study
• помогать людям понимать — to help people understand
• помогать людям доверять друг другу — to help people trust each other

English often has to before the second verb, but Russian simply uses the infinitive.

Друг другу means each other.

It is a common Russian way to express reciprocal action, when two or more people do something mutually.

Examples:

• они помогают друг другу — they help each other
• они верят друг другу — they believe each other
• они доверяют друг другу — they trust each other

So in this sentence, друг другу shows that the people trust one another, not just some outside person.

Because the phrase друг друг- changes by case, just like a normal noun phrase.

The verb доверять requires the dative:

доверять кому? — to trust whom?

So the reciprocal phrase must also be in the dative:

• друг другу — to each other

Compare:

• видеть друг друга — to see each other
  because видеть takes the accusative
• помогать друг другу — to help each other
  because помогать takes the dative
• гордиться друг другом — to be proud of each other
  because гордиться takes the instrumental

They do both refer to people, but they do different jobs in the sentence.

• людям = the people who receive the help
• друг другу = the people whom they trust, in a mutual relationship

So the logic is:

Honesty helps people
do what?
trust each other

If you remove людям, the sentence becomes less explicit about who is being helped.

Because Russian uses the present tense for general truths and usual facts, just like English does.

So Честность помогает людям доверять друг другу is not only about what is happening right now. It means something general:

Honesty helps people trust each other
as a general principle.

This is a very normal use of the present tense in Russian.

Both are imperfective:

• помогает comes from помогать
• доверять is also imperfective

That makes sense because the sentence expresses a general, ongoing idea, not one completed single event.

Imperfective is natural here because the meaning is something like:

• honesty generally helps
• trusting is a process or state

If you used a perfective verb, the meaning would change and sound more like a one-time completed action.

Because after помогать, Russian very often uses a direct infinitive:

помогать кому-то делать что-то

That is the normal, compact structure.

So:

• помогает людям доверять — helps people trust

Using чтобы would require a different construction, with a full clause, and it would usually sound heavier or change the nuance.

In this sentence, the infinitive is the most natural choice.

Yes, Russian word order is flexible because the cases show the grammatical roles.

The version here is the most neutral and natural:

Честность помогает людям доверять друг другу.

You can move things around for emphasis, for example:

• Людям честность помогает доверять друг другу.
  This puts more focus on people.

But not every rearrangement sounds equally natural. Russian word order is flexible, but it is not random.

For a learner, the original order is the best one to copy.

This is a very good nuance question.

• доверять = to trust
• верить = to believe

These can overlap, but they are not identical.

• верить друг другу often means to believe each other’s words
• доверять друг другу is broader: to trust each other in general

In this sentence, доверять is the better choice because the idea is about mutual trust, not just believing what someone says.